Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,3,Mod(19,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.d (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.67030659073\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.19 |
Dual form | 98.3.d.a.31.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 1.22474i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.621320 | + | 0.358719i | −0.207107 | + | 0.119573i | −0.599966 | − | 0.800025i | \(-0.704819\pi\) |
0.392859 | + | 0.919599i | \(0.371486\pi\) | |||||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | 5.74264 | + | 3.31552i | 1.14853 | + | 0.663103i | 0.948528 | − | 0.316693i | \(-0.102572\pi\) |
0.200000 | + | 0.979796i | \(0.435906\pi\) | |||||||
\(6\) | − | 1.01461i | − | 0.169102i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −4.24264 | + | 7.34847i | −0.471405 | + | 0.816497i | ||||
\(10\) | −8.12132 | + | 4.68885i | −0.812132 | + | 0.468885i | ||||
\(11\) | 2.37868 | + | 4.11999i | 0.216244 | + | 0.374545i | 0.953657 | − | 0.300897i | \(-0.0972861\pi\) |
−0.737413 | + | 0.675442i | \(0.763953\pi\) | |||||||
\(12\) | 1.24264 | + | 0.717439i | 0.103553 | + | 0.0597866i | ||||
\(13\) | 15.2913i | 1.17625i | 0.808769 | + | 0.588126i | \(0.200134\pi\) | ||||
−0.808769 | + | 0.588126i | \(0.799866\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.75736 | −0.317157 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.25736 | − | 1.88064i | 0.191609 | − | 0.110626i | −0.401126 | − | 0.916023i | \(-0.631381\pi\) |
0.592736 | + | 0.805397i | \(0.298048\pi\) | |||||||
\(18\) | −6.00000 | − | 10.3923i | −0.333333 | − | 0.577350i | ||||
\(19\) | −3.62132 | − | 2.09077i | −0.190596 | − | 0.110041i | 0.401666 | − | 0.915786i | \(-0.368431\pi\) |
−0.592261 | + | 0.805746i | \(0.701765\pi\) | |||||||
\(20\) | − | 13.2621i | − | 0.663103i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.72792 | −0.305815 | ||||||||
\(23\) | 13.8640 | − | 24.0131i | 0.602781 | − | 1.04405i | −0.389617 | − | 0.920977i | \(-0.627393\pi\) |
0.992398 | − | 0.123070i | \(-0.0392740\pi\) | |||||||
\(24\) | −1.75736 | + | 1.01461i | −0.0732233 | + | 0.0422755i | ||||
\(25\) | 9.48528 | + | 16.4290i | 0.379411 | + | 0.657160i | ||||
\(26\) | −18.7279 | − | 10.8126i | −0.720305 | − | 0.415868i | ||||
\(27\) | − | 12.5446i | − | 0.464616i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.51472 | 0.121197 | 0.0605986 | − | 0.998162i | \(-0.480699\pi\) | ||||
0.0605986 | + | 0.998162i | \(0.480699\pi\) | |||||||
\(30\) | 3.36396 | − | 5.82655i | 0.112132 | − | 0.194218i | ||||
\(31\) | 42.3198 | − | 24.4334i | 1.36516 | − | 0.788173i | 0.374850 | − | 0.927085i | \(-0.377694\pi\) |
0.990305 | + | 0.138913i | \(0.0443607\pi\) | |||||||
\(32\) | −2.82843 | − | 4.89898i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −2.95584 | − | 1.70656i | −0.0895710 | − | 0.0517139i | ||||
\(34\) | 5.31925i | 0.156448i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 16.9706 | 0.471405 | ||||||||
\(37\) | 1.47056 | − | 2.54709i | 0.0397449 | − | 0.0688403i | −0.845469 | − | 0.534025i | \(-0.820679\pi\) |
0.885214 | + | 0.465185i | \(0.154012\pi\) | |||||||
\(38\) | 5.12132 | − | 2.95680i | 0.134772 | − | 0.0778104i | ||||
\(39\) | −5.48528 | − | 9.50079i | −0.140648 | − | 0.243610i | ||||
\(40\) | 16.2426 | + | 9.37769i | 0.406066 | + | 0.234442i | ||||
\(41\) | − | 27.9590i | − | 0.681927i | −0.940077 | − | 0.340963i | \(-0.889247\pi\) | ||
0.940077 | − | 0.340963i | \(-0.110753\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4853 | −0.243844 | −0.121922 | − | 0.992540i | \(-0.538906\pi\) | ||||
−0.121922 | + | 0.992540i | \(0.538906\pi\) | |||||||
\(44\) | 4.75736 | − | 8.23999i | 0.108122 | − | 0.187272i | ||||
\(45\) | −48.7279 | + | 28.1331i | −1.08284 | + | 0.625180i | ||||
\(46\) | 19.6066 | + | 33.9596i | 0.426230 | + | 0.738253i | ||||
\(47\) | −45.6213 | − | 26.3395i | −0.970666 | − | 0.560415i | −0.0712271 | − | 0.997460i | \(-0.522691\pi\) |
−0.899439 | + | 0.437046i | \(0.856025\pi\) | |||||||
\(48\) | − | 2.86976i | − | 0.0597866i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −26.8284 | −0.536569 | ||||||||
\(51\) | −1.34924 | + | 2.33696i | −0.0264557 | + | 0.0458227i | ||||
\(52\) | 26.4853 | − | 15.2913i | 0.509332 | − | 0.294063i | ||||
\(53\) | −27.9853 | − | 48.4719i | −0.528024 | − | 0.914565i | −0.999466 | − | 0.0326677i | \(-0.989600\pi\) |
0.471442 | − | 0.881897i | \(-0.343734\pi\) | |||||||
\(54\) | 15.3640 | + | 8.87039i | 0.284518 | + | 0.164266i | ||||
\(55\) | 31.5462i | 0.573567i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.0526316 | ||||||||
\(58\) | −2.48528 | + | 4.30463i | −0.0428497 | + | 0.0742178i | ||||
\(59\) | −33.5330 | + | 19.3603i | −0.568356 | + | 0.328141i | −0.756492 | − | 0.654002i | \(-0.773089\pi\) |
0.188136 | + | 0.982143i | \(0.439755\pi\) | |||||||
\(60\) | 4.75736 | + | 8.23999i | 0.0792893 | + | 0.137333i | ||||
\(61\) | 78.3823 | + | 45.2540i | 1.28495 | + | 0.741869i | 0.977750 | − | 0.209774i | \(-0.0672729\pi\) |
0.307205 | + | 0.951643i | \(0.400606\pi\) | |||||||
\(62\) | 69.1080i | 1.11464i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −50.6985 | + | 87.8124i | −0.779977 | + | 1.35096i | ||||
\(66\) | 4.18019 | − | 2.41344i | 0.0633363 | − | 0.0365672i | ||||
\(67\) | 17.3198 | + | 29.9988i | 0.258505 | + | 0.447743i | 0.965842 | − | 0.259134i | \(-0.0834370\pi\) |
−0.707337 | + | 0.706877i | \(0.750104\pi\) | |||||||
\(68\) | −6.51472 | − | 3.76127i | −0.0958047 | − | 0.0553129i | ||||
\(69\) | 19.8931i | 0.288306i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36.4264 | 0.513048 | 0.256524 | − | 0.966538i | \(-0.417423\pi\) | ||||
0.256524 | + | 0.966538i | \(0.417423\pi\) | |||||||
\(72\) | −12.0000 | + | 20.7846i | −0.166667 | + | 0.288675i | ||||
\(73\) | −45.5589 | + | 26.3034i | −0.624094 | + | 0.360321i | −0.778461 | − | 0.627693i | \(-0.783999\pi\) |
0.154367 | + | 0.988014i | \(0.450666\pi\) | |||||||
\(74\) | 2.07969 | + | 3.60213i | 0.0281039 | + | 0.0486774i | ||||
\(75\) | −11.7868 | − | 6.80511i | −0.157157 | − | 0.0907348i | ||||
\(76\) | 8.36308i | 0.110041i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 15.5147 | 0.198907 | ||||||||
\(79\) | 16.8934 | − | 29.2602i | 0.213840 | − | 0.370383i | −0.739073 | − | 0.673626i | \(-0.764736\pi\) |
0.952913 | + | 0.303243i | \(0.0980694\pi\) | |||||||
\(80\) | −22.9706 | + | 13.2621i | −0.287132 | + | 0.165776i | ||||
\(81\) | −33.6838 | − | 58.3420i | −0.415849 | − | 0.720272i | ||||
\(82\) | 34.2426 | + | 19.7700i | 0.417593 | + | 0.241098i | ||||
\(83\) | − | 127.577i | − | 1.53708i | −0.639803 | − | 0.768539i | \(-0.720984\pi\) | ||
0.639803 | − | 0.768539i | \(-0.279016\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.9411 | 0.293425 | ||||||||
\(86\) | 7.41421 | − | 12.8418i | 0.0862118 | − | 0.149323i | ||||
\(87\) | −2.18377 | + | 1.26080i | −0.0251008 | + | 0.0144919i | ||||
\(88\) | 6.72792 | + | 11.6531i | 0.0764537 | + | 0.132422i | ||||
\(89\) | 43.5883 | + | 25.1657i | 0.489756 | + | 0.282761i | 0.724473 | − | 0.689303i | \(-0.242083\pi\) |
−0.234717 | + | 0.972064i | \(0.575416\pi\) | |||||||
\(90\) | − | 79.5724i | − | 0.884137i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −55.4558 | −0.602781 | ||||||||
\(93\) | −17.5294 | + | 30.3619i | −0.188489 | + | 0.326472i | ||||
\(94\) | 64.5183 | − | 37.2497i | 0.686365 | − | 0.396273i | ||||
\(95\) | −13.8640 | − | 24.0131i | −0.145936 | − | 0.252769i | ||||
\(96\) | 3.51472 | + | 2.02922i | 0.0366117 | + | 0.0211377i | ||||
\(97\) | 101.792i | 1.04940i | 0.851287 | + | 0.524700i | \(0.175823\pi\) | ||||
−0.851287 | + | 0.524700i | \(0.824177\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −40.3675 | −0.407753 | ||||||||
\(100\) | 18.9706 | − | 32.8580i | 0.189706 | − | 0.328580i | ||||
\(101\) | 51.6838 | − | 29.8396i | 0.511720 | − | 0.295442i | −0.221820 | − | 0.975088i | \(-0.571200\pi\) |
0.733541 | + | 0.679646i | \(0.237866\pi\) | |||||||
\(102\) | −1.90812 | − | 3.30496i | −0.0187070 | − | 0.0324015i | ||||
\(103\) | −104.077 | − | 60.0890i | −1.01046 | − | 0.583388i | −0.0991322 | − | 0.995074i | \(-0.531607\pi\) |
−0.911326 | + | 0.411686i | \(0.864940\pi\) | |||||||
\(104\) | 43.2503i | 0.415868i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 79.1543 | 0.746739 | ||||||||
\(107\) | 56.8051 | − | 98.3893i | 0.530889 | − | 0.919526i | −0.468462 | − | 0.883484i | \(-0.655192\pi\) |
0.999350 | − | 0.0360423i | \(-0.0114751\pi\) | |||||||
\(108\) | −21.7279 | + | 12.5446i | −0.201184 | + | 0.116154i | ||||
\(109\) | 72.6543 | + | 125.841i | 0.666553 | + | 1.15450i | 0.978862 | + | 0.204524i | \(0.0655645\pi\) |
−0.312308 | + | 0.949981i | \(0.601102\pi\) | |||||||
\(110\) | −38.6360 | − | 22.3065i | −0.351237 | − | 0.202787i | ||||
\(111\) | 2.11008i | 0.0190097i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 34.5442 | 0.305700 | 0.152850 | − | 0.988249i | \(-0.451155\pi\) | ||||
0.152850 | + | 0.988249i | \(0.451155\pi\) | |||||||
\(114\) | −2.12132 | + | 3.67423i | −0.0186081 | + | 0.0322301i | ||||
\(115\) | 159.231 | − | 91.9323i | 1.38462 | − | 0.799412i | ||||
\(116\) | −3.51472 | − | 6.08767i | −0.0302993 | − | 0.0524799i | ||||
\(117\) | −112.368 | − | 64.8754i | −0.960406 | − | 0.554491i | ||||
\(118\) | − | 54.7592i | − | 0.464061i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −13.4558 | −0.112132 | ||||||||
\(121\) | 49.1838 | − | 85.1888i | 0.406477 | − | 0.704040i | ||||
\(122\) | −110.849 | + | 63.9988i | −0.908600 | + | 0.524581i | ||||
\(123\) | 10.0294 | + | 17.3715i | 0.0815401 | + | 0.141232i | ||||
\(124\) | −84.6396 | − | 48.8667i | −0.682578 | − | 0.394086i | ||||
\(125\) | − | 39.9814i | − | 0.319851i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −247.338 | −1.94754 | −0.973772 | − | 0.227526i | \(-0.926936\pi\) | ||||
−0.973772 | + | 0.227526i | \(0.926936\pi\) | |||||||
\(128\) | −5.65685 | + | 9.79796i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 6.51472 | − | 3.76127i | 0.0505017 | − | 0.0291572i | ||||
\(130\) | −71.6985 | − | 124.185i | −0.551527 | − | 0.955272i | ||||
\(131\) | 127.864 | + | 73.8223i | 0.976061 | + | 0.563529i | 0.901079 | − | 0.433656i | \(-0.142777\pi\) |
0.0749822 | + | 0.997185i | \(0.476110\pi\) | |||||||
\(132\) | 6.82623i | 0.0517139i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −48.9878 | −0.365581 | ||||||||
\(135\) | 41.5919 | − | 72.0393i | 0.308088 | − | 0.533624i | ||||
\(136\) | 9.21320 | − | 5.31925i | 0.0677441 | − | 0.0391121i | ||||
\(137\) | 16.2868 | + | 28.2096i | 0.118882 | + | 0.205909i | 0.919325 | − | 0.393500i | \(-0.128736\pi\) |
−0.800443 | + | 0.599409i | \(0.795402\pi\) | |||||||
\(138\) | −24.3640 | − | 14.0665i | −0.176550 | − | 0.101931i | ||||
\(139\) | 68.5857i | 0.493422i | 0.969089 | + | 0.246711i | \(0.0793499\pi\) | ||||
−0.969089 | + | 0.246711i | \(0.920650\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37.7939 | 0.268042 | ||||||||
\(142\) | −25.7574 | + | 44.6131i | −0.181390 | + | 0.314176i | ||||
\(143\) | −63.0000 | + | 36.3731i | −0.440559 | + | 0.254357i | ||||
\(144\) | −16.9706 | − | 29.3939i | −0.117851 | − | 0.204124i | ||||
\(145\) | 20.1838 | + | 11.6531i | 0.139198 | + | 0.0803662i | ||||
\(146\) | − | 74.3973i | − | 0.509571i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.88225 | −0.0397449 | ||||||||
\(149\) | −46.1985 | + | 80.0181i | −0.310057 | + | 0.537034i | −0.978374 | − | 0.206842i | \(-0.933681\pi\) |
0.668317 | + | 0.743876i | \(0.267015\pi\) | |||||||
\(150\) | 16.6690 | − | 9.62388i | 0.111127 | − | 0.0641592i | ||||
\(151\) | 45.8934 | + | 79.4897i | 0.303930 | + | 0.526422i | 0.977022 | − | 0.213136i | \(-0.0683678\pi\) |
−0.673093 | + | 0.739558i | \(0.735035\pi\) | |||||||
\(152\) | −10.2426 | − | 5.91359i | −0.0673858 | − | 0.0389052i | ||||
\(153\) | 31.9155i | 0.208598i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 324.037 | 2.09056 | ||||||||
\(156\) | −10.9706 | + | 19.0016i | −0.0703241 | + | 0.121805i | ||||
\(157\) | −7.32338 | + | 4.22815i | −0.0466457 | + | 0.0269309i | −0.523142 | − | 0.852246i | \(-0.675240\pi\) |
0.476496 | + | 0.879177i | \(0.341907\pi\) | |||||||
\(158\) | 23.8909 | + | 41.3802i | 0.151208 | + | 0.261900i | ||||
\(159\) | 34.7756 | + | 20.0777i | 0.218715 | + | 0.126275i | ||||
\(160\) | − | 37.5108i | − | 0.234442i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 95.2721 | 0.588099 | ||||||||
\(163\) | −110.989 | + | 192.238i | −0.680913 | + | 1.17938i | 0.293789 | + | 0.955870i | \(0.405084\pi\) |
−0.974703 | + | 0.223506i | \(0.928250\pi\) | |||||||
\(164\) | −48.4264 | + | 27.9590i | −0.295283 | + | 0.170482i | ||||
\(165\) | −11.3162 | − | 19.6003i | −0.0685832 | − | 0.118790i | ||||
\(166\) | 156.250 | + | 90.2109i | 0.941264 | + | 0.543439i | ||||
\(167\) | 168.841i | 1.01102i | 0.862820 | + | 0.505511i | \(0.168696\pi\) | ||||
−0.862820 | + | 0.505511i | \(0.831304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −64.8234 | −0.383570 | ||||||||
\(170\) | −17.6360 | + | 30.5465i | −0.103741 | + | 0.179685i | ||||
\(171\) | 30.7279 | − | 17.7408i | 0.179695 | − | 0.103747i | ||||
\(172\) | 10.4853 | + | 18.1610i | 0.0609609 | + | 0.105587i | ||||
\(173\) | 142.323 | + | 82.1704i | 0.822678 | + | 0.474974i | 0.851339 | − | 0.524616i | \(-0.175791\pi\) |
−0.0286608 | + | 0.999589i | \(0.509124\pi\) | |||||||
\(174\) | − | 3.56608i | − | 0.0204947i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.0294 | −0.108122 | ||||||||
\(177\) | 13.8898 | − | 24.0579i | 0.0784736 | − | 0.135920i | ||||
\(178\) | −61.6432 | + | 35.5897i | −0.346310 | + | 0.199942i | ||||
\(179\) | −92.5919 | − | 160.374i | −0.517273 | − | 0.895943i | −0.999799 | − | 0.0200614i | \(-0.993614\pi\) |
0.482526 | − | 0.875882i | \(-0.339720\pi\) | |||||||
\(180\) | 97.4558 | + | 56.2662i | 0.541421 | + | 0.312590i | ||||
\(181\) | − | 155.086i | − | 0.856830i | −0.903582 | − | 0.428415i | \(-0.859072\pi\) | ||
0.903582 | − | 0.428415i | \(-0.140928\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −64.9340 | −0.354831 | ||||||||
\(184\) | 39.2132 | − | 67.9193i | 0.213115 | − | 0.369126i | ||||
\(185\) | 16.8898 | − | 9.75135i | 0.0912964 | − | 0.0527100i | ||||
\(186\) | −24.7904 | − | 42.9382i | −0.133282 | − | 0.230850i | ||||
\(187\) | 15.4964 | + | 8.94687i | 0.0828686 | + | 0.0478442i | ||||
\(188\) | 105.358i | 0.560415i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 39.2132 | 0.206385 | ||||||||
\(191\) | −124.048 | + | 214.857i | −0.649465 | + | 1.12491i | 0.333786 | + | 0.942649i | \(0.391674\pi\) |
−0.983251 | + | 0.182257i | \(0.941660\pi\) | |||||||
\(192\) | −4.97056 | + | 2.86976i | −0.0258883 | + | 0.0149466i | ||||
\(193\) | −77.1690 | − | 133.661i | −0.399840 | − | 0.692543i | 0.593866 | − | 0.804564i | \(-0.297601\pi\) |
−0.993706 | + | 0.112021i | \(0.964268\pi\) | |||||||
\(194\) | −124.669 | − | 71.9777i | −0.642624 | − | 0.371019i | ||||
\(195\) | − | 72.7461i | − | 0.373057i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −181.103 | −0.919303 | −0.459651 | − | 0.888099i | \(-0.652026\pi\) | ||||
−0.459651 | + | 0.888099i | \(0.652026\pi\) | |||||||
\(198\) | 28.5442 | − | 49.4399i | 0.144162 | − | 0.249697i | ||||
\(199\) | −301.989 | + | 174.353i | −1.51753 | + | 0.876147i | −0.517744 | + | 0.855535i | \(0.673228\pi\) |
−0.999788 | + | 0.0206121i | \(0.993439\pi\) | |||||||
\(200\) | 26.8284 | + | 46.4682i | 0.134142 | + | 0.232341i | ||||
\(201\) | −21.5223 | − | 12.4259i | −0.107076 | − | 0.0618204i | ||||
\(202\) | 84.3992i | 0.417818i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.39697 | 0.0264557 | ||||||||
\(205\) | 92.6985 | − | 160.558i | 0.452188 | − | 0.783212i | ||||
\(206\) | 147.187 | − | 84.9786i | 0.714502 | − | 0.412518i | ||||
\(207\) | 117.640 | + | 203.758i | 0.568307 | + | 0.984337i | ||||
\(208\) | −52.9706 | − | 30.5826i | −0.254666 | − | 0.147032i | ||||
\(209\) | − | 19.8931i | − | 0.0951823i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 364.073 | 1.72547 | 0.862733 | − | 0.505660i | \(-0.168751\pi\) | ||||
0.862733 | + | 0.505660i | \(0.168751\pi\) | |||||||
\(212\) | −55.9706 | + | 96.9439i | −0.264012 | + | 0.457282i | ||||
\(213\) | −22.6325 | + | 13.0669i | −0.106256 | + | 0.0613468i | ||||
\(214\) | 80.3345 | + | 139.143i | 0.375395 | + | 0.650203i | ||||
\(215\) | −60.2132 | − | 34.7641i | −0.280061 | − | 0.161694i | ||||
\(216\) | − | 35.4815i | − | 0.164266i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −205.497 | −0.942649 | ||||||||
\(219\) | 18.8711 | − | 32.6857i | 0.0861694 | − | 0.149250i | ||||
\(220\) | 54.6396 | − | 31.5462i | 0.248362 | − | 0.143392i | ||||
\(221\) | 28.7574 | + | 49.8092i | 0.130124 | + | 0.225381i | ||||
\(222\) | −2.58431 | − | 1.49205i | −0.0116410 | − | 0.00672095i | ||||
\(223\) | 123.231i | 0.552603i | 0.961071 | + | 0.276302i | \(0.0891089\pi\) | ||||
−0.961071 | + | 0.276302i | \(0.910891\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −160.971 | −0.715425 | ||||||||
\(226\) | −24.4264 | + | 42.3078i | −0.108081 | + | 0.187203i | ||||
\(227\) | 66.1432 | − | 38.1878i | 0.291380 | − | 0.168228i | −0.347184 | − | 0.937797i | \(-0.612862\pi\) |
0.638564 | + | 0.769569i | \(0.279529\pi\) | |||||||
\(228\) | −3.00000 | − | 5.19615i | −0.0131579 | − | 0.0227901i | ||||
\(229\) | −309.419 | − | 178.643i | −1.35117 | − | 0.780101i | −0.362760 | − | 0.931883i | \(-0.618166\pi\) |
−0.988414 | + | 0.151782i | \(0.951499\pi\) | |||||||
\(230\) | 260.024i | 1.13054i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.94113 | 0.0428497 | ||||||||
\(233\) | 136.537 | − | 236.488i | 0.585994 | − | 1.01497i | −0.408757 | − | 0.912643i | \(-0.634038\pi\) |
0.994751 | − | 0.102328i | \(-0.0326291\pi\) | |||||||
\(234\) | 158.912 | − | 91.7477i | 0.679110 | − | 0.392084i | ||||
\(235\) | −174.658 | − | 302.516i | −0.743225 | − | 1.28730i | ||||
\(236\) | 67.0660 | + | 38.7206i | 0.284178 | + | 0.164070i | ||||
\(237\) | 24.2400i | 0.102278i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −265.103 | −1.10922 | −0.554608 | − | 0.832112i | \(-0.687132\pi\) | ||||
−0.554608 | + | 0.832112i | \(0.687132\pi\) | |||||||
\(240\) | 9.51472 | − | 16.4800i | 0.0396447 | − | 0.0686666i | ||||
\(241\) | 75.8970 | − | 43.8191i | 0.314925 | − | 0.181822i | −0.334203 | − | 0.942501i | \(-0.608467\pi\) |
0.649128 | + | 0.760679i | \(0.275134\pi\) | |||||||
\(242\) | 69.5563 | + | 120.475i | 0.287423 | + | 0.497831i | ||||
\(243\) | 139.632 | + | 80.6168i | 0.574619 | + | 0.331757i | ||||
\(244\) | − | 181.016i | − | 0.741869i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −28.3675 | −0.115315 | ||||||||
\(247\) | 31.9706 | − | 55.3746i | 0.129435 | − | 0.224189i | ||||
\(248\) | 119.698 | − | 69.1080i | 0.482655 | − | 0.278661i | ||||
\(249\) | 45.7645 | + | 79.2664i | 0.183793 | + | 0.318339i | ||||
\(250\) | 48.9670 | + | 28.2711i | 0.195868 | + | 0.113084i | ||||
\(251\) | − | 495.655i | − | 1.97472i | −0.158491 | − | 0.987360i | \(-0.550663\pi\) | ||
0.158491 | − | 0.987360i | \(-0.449337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 131.912 | 0.521390 | ||||||||
\(254\) | 174.894 | − | 302.926i | 0.688561 | − | 1.19262i | ||||
\(255\) | −15.4964 | + | 8.94687i | −0.0607703 | + | 0.0350858i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −346.875 | − | 200.268i | −1.34971 | − | 0.779254i | −0.361499 | − | 0.932372i | \(-0.617735\pi\) |
−0.988208 | + | 0.153119i | \(0.951068\pi\) | |||||||
\(258\) | 10.6385i | 0.0412345i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 202.794 | 0.779977 | ||||||||
\(261\) | −14.9117 | + | 25.8278i | −0.0571329 | + | 0.0989571i | ||||
\(262\) | −180.827 | + | 104.400i | −0.690179 | + | 0.398475i | ||||
\(263\) | 16.1726 | + | 28.0118i | 0.0614928 | + | 0.106509i | 0.895133 | − | 0.445799i | \(-0.147081\pi\) |
−0.833640 | + | 0.552308i | \(0.813747\pi\) | |||||||
\(264\) | −8.36039 | − | 4.82687i | −0.0316681 | − | 0.0182836i | ||||
\(265\) | − | 371.142i | − | 1.40054i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −36.1097 | −0.135242 | ||||||||
\(268\) | 34.6396 | − | 59.9976i | 0.129252 | − | 0.223872i | ||||
\(269\) | 265.838 | − | 153.482i | 0.988246 | − | 0.570564i | 0.0834963 | − | 0.996508i | \(-0.473391\pi\) |
0.904749 | + | 0.425944i | \(0.140058\pi\) | |||||||
\(270\) | 58.8198 | + | 101.879i | 0.217851 | + | 0.377329i | ||||
\(271\) | 65.8051 | + | 37.9926i | 0.242823 | + | 0.140194i | 0.616474 | − | 0.787376i | \(-0.288561\pi\) |
−0.373650 | + | 0.927570i | \(0.621894\pi\) | |||||||
\(272\) | 15.0451i | 0.0553129i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −46.0660 | −0.168124 | ||||||||
\(275\) | −45.1249 | + | 78.1586i | −0.164091 | + | 0.284213i | ||||
\(276\) | 34.4558 | − | 19.8931i | 0.124840 | − | 0.0720764i | ||||
\(277\) | −139.206 | − | 241.111i | −0.502547 | − | 0.870438i | −0.999996 | − | 0.00294398i | \(-0.999063\pi\) |
0.497448 | − | 0.867494i | \(-0.334270\pi\) | |||||||
\(278\) | −84.0000 | − | 48.4974i | −0.302158 | − | 0.174451i | ||||
\(279\) | 414.648i | 1.48619i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 394.690 | 1.40459 | 0.702296 | − | 0.711885i | \(-0.252158\pi\) | ||||
0.702296 | + | 0.711885i | \(0.252158\pi\) | |||||||
\(282\) | −26.7244 | + | 46.2879i | −0.0947672 | + | 0.164142i | ||||
\(283\) | −126.783 | + | 73.1981i | −0.447996 | + | 0.258650i | −0.706983 | − | 0.707230i | \(-0.749944\pi\) |
0.258988 | + | 0.965881i | \(0.416611\pi\) | |||||||
\(284\) | −36.4264 | − | 63.0924i | −0.128262 | − | 0.222156i | ||||
\(285\) | 17.2279 | + | 9.94655i | 0.0604488 | + | 0.0349002i | ||||
\(286\) | − | 102.879i | − | 0.359715i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 48.0000 | 0.166667 | ||||||||
\(289\) | −137.426 | + | 238.030i | −0.475524 | + | 0.823632i | ||||
\(290\) | −28.5442 | + | 16.4800i | −0.0984281 | + | 0.0568275i | ||||
\(291\) | −36.5147 | − | 63.2453i | −0.125480 | − | 0.217338i | ||||
\(292\) | 91.1177 | + | 52.6069i | 0.312047 | + | 0.180160i | ||||
\(293\) | 299.678i | 1.02279i | 0.859345 | + | 0.511396i | \(0.170872\pi\) | ||||
−0.859345 | + | 0.511396i | \(0.829128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −256.757 | −0.870364 | ||||||||
\(296\) | 4.15938 | − | 7.20426i | 0.0140520 | − | 0.0243387i | ||||
\(297\) | 51.6838 | − | 29.8396i | 0.174019 | − | 0.100470i | ||||
\(298\) | −65.3345 | − | 113.163i | −0.219243 | − | 0.379741i | ||||
\(299\) | 367.191 | + | 211.998i | 1.22806 | + | 0.709023i | ||||
\(300\) | 27.2204i | 0.0907348i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −129.806 | −0.429822 | ||||||||
\(303\) | −21.4081 | + | 37.0799i | −0.0706539 | + | 0.122376i | ||||
\(304\) | 14.4853 | − | 8.36308i | 0.0476490 | − | 0.0275101i | ||||
\(305\) | 300.081 | + | 519.755i | 0.983871 | + | 1.70412i | ||||
\(306\) | −39.0883 | − | 22.5676i | −0.127740 | − | 0.0737505i | ||||
\(307\) | − | 20.9886i | − | 0.0683666i | −0.999416 | − | 0.0341833i | \(-0.989117\pi\) | ||
0.999416 | − | 0.0341833i | \(-0.0108830\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 86.2203 | 0.279030 | ||||||||
\(310\) | −229.128 | + | 396.862i | −0.739124 | + | 1.28020i | ||||
\(311\) | −157.651 | + | 91.0197i | −0.506916 | + | 0.292668i | −0.731565 | − | 0.681772i | \(-0.761210\pi\) |
0.224649 | + | 0.974440i | \(0.427876\pi\) | |||||||
\(312\) | −15.5147 | − | 26.8723i | −0.0497267 | − | 0.0861291i | ||||
\(313\) | 84.8087 | + | 48.9643i | 0.270954 | + | 0.156435i | 0.629321 | − | 0.777145i | \(-0.283333\pi\) |
−0.358367 | + | 0.933581i | \(0.616666\pi\) | |||||||
\(314\) | − | 11.9590i | − | 0.0380861i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −67.5736 | −0.213840 | ||||||||
\(317\) | 240.985 | − | 417.399i | 0.760206 | − | 1.31672i | −0.182538 | − | 0.983199i | \(-0.558431\pi\) |
0.942744 | − | 0.333517i | \(-0.108235\pi\) | |||||||
\(318\) | −49.1802 | + | 28.3942i | −0.154655 | + | 0.0892899i | ||||
\(319\) | 8.36039 | + | 14.4806i | 0.0262081 | + | 0.0453938i | ||||
\(320\) | 45.9411 | + | 26.5241i | 0.143566 | + | 0.0828879i | ||||
\(321\) | 81.5084i | 0.253920i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.7279 | −0.0486933 | ||||||||
\(324\) | −67.3675 | + | 116.684i | −0.207924 | + | 0.360136i | ||||
\(325\) | −251.220 | + | 145.042i | −0.772986 | + | 0.446283i | ||||
\(326\) | −156.962 | − | 271.866i | −0.481478 | − | 0.833945i | ||||
\(327\) | −90.2832 | − | 52.1250i | −0.276095 | − | 0.159404i | ||||
\(328\) | − | 79.0800i | − | 0.241098i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 32.0071 | 0.0969913 | ||||||||
\(331\) | −112.504 | + | 194.862i | −0.339890 | + | 0.588707i | −0.984412 | − | 0.175879i | \(-0.943723\pi\) |
0.644522 | + | 0.764586i | \(0.277056\pi\) | |||||||
\(332\) | −220.971 | + | 127.577i | −0.665574 | + | 0.384269i | ||||
\(333\) | 12.4781 | + | 21.6128i | 0.0374719 | + | 0.0649032i | ||||
\(334\) | −206.787 | − | 119.388i | −0.619122 | − | 0.357450i | ||||
\(335\) | 229.696i | 0.685661i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −264.368 | −0.784473 | −0.392237 | − | 0.919864i | \(-0.628299\pi\) | ||||
−0.392237 | + | 0.919864i | \(0.628299\pi\) | |||||||
\(338\) | 45.8370 | − | 79.3921i | 0.135613 | − | 0.234888i | ||||
\(339\) | −21.4630 | + | 12.3917i | −0.0633126 | + | 0.0365536i | ||||
\(340\) | −24.9411 | − | 43.1993i | −0.0733563 | − | 0.127057i | ||||
\(341\) | 201.331 | + | 116.238i | 0.590412 | + | 0.340875i | ||||
\(342\) | 50.1785i | 0.146721i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −29.6569 | −0.0862118 | ||||||||
\(345\) | −65.9558 | + | 114.239i | −0.191176 | + | 0.331127i | ||||
\(346\) | −201.276 | + | 116.207i | −0.581722 | + | 0.335857i | ||||
\(347\) | 95.6285 | + | 165.633i | 0.275586 | + | 0.477330i | 0.970283 | − | 0.241973i | \(-0.0777947\pi\) |
−0.694697 | + | 0.719303i | \(0.744461\pi\) | |||||||
\(348\) | 4.36753 | + | 2.52160i | 0.0125504 | + | 0.00724597i | ||||
\(349\) | 135.448i | 0.388104i | 0.980991 | + | 0.194052i | \(0.0621630\pi\) | ||||
−0.980991 | + | 0.194052i | \(0.937837\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 191.823 | 0.546505 | ||||||||
\(352\) | 13.4558 | − | 23.3062i | 0.0382268 | − | 0.0662108i | ||||
\(353\) | 301.802 | − | 174.245i | 0.854962 | − | 0.493612i | −0.00736010 | − | 0.999973i | \(-0.502343\pi\) |
0.862322 | + | 0.506360i | \(0.169009\pi\) | |||||||
\(354\) | 19.6432 | + | 34.0230i | 0.0554892 | + | 0.0961101i | ||||
\(355\) | 209.184 | + | 120.772i | 0.589250 | + | 0.340204i | ||||
\(356\) | − | 100.663i | − | 0.282761i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 261.889 | 0.731535 | ||||||||
\(359\) | −152.415 | + | 263.991i | −0.424555 | + | 0.735351i | −0.996379 | − | 0.0850256i | \(-0.972903\pi\) |
0.571824 | + | 0.820377i | \(0.306236\pi\) | |||||||
\(360\) | −137.823 | + | 79.5724i | −0.382843 | + | 0.221034i | ||||
\(361\) | −171.757 | − | 297.492i | −0.475782 | − | 0.824079i | ||||
\(362\) | 189.941 | + | 109.663i | 0.524699 | + | 0.302935i | ||||
\(363\) | 70.5727i | 0.194415i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −348.838 | −0.955720 | ||||||||
\(366\) | 45.9153 | − | 79.5276i | 0.125452 | − | 0.217288i | ||||
\(367\) | 82.2761 | − | 47.5021i | 0.224186 | − | 0.129434i | −0.383701 | − | 0.923457i | \(-0.625351\pi\) |
0.607887 | + | 0.794024i | \(0.292017\pi\) | |||||||
\(368\) | 55.4558 | + | 96.0523i | 0.150695 | + | 0.261012i | ||||
\(369\) | 205.456 | + | 118.620i | 0.556791 | + | 0.321463i | ||||
\(370\) | 27.5810i | 0.0745432i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 70.1177 | 0.188489 | ||||||||
\(373\) | −126.779 | + | 219.588i | −0.339891 | + | 0.588708i | −0.984412 | − | 0.175879i | \(-0.943723\pi\) |
0.644521 | + | 0.764586i | \(0.277057\pi\) | |||||||
\(374\) | −21.9153 | + | 12.6528i | −0.0585970 | + | 0.0338310i | ||||
\(375\) | 14.3421 | + | 24.8412i | 0.0382456 | + | 0.0662433i | ||||
\(376\) | −129.037 | − | 74.4993i | −0.343182 | − | 0.198136i | ||||
\(377\) | 53.7446i | 0.142559i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 508.250 | 1.34103 | 0.670514 | − | 0.741897i | \(-0.266074\pi\) | ||||
0.670514 | + | 0.741897i | \(0.266074\pi\) | |||||||
\(380\) | −27.7279 | + | 48.0262i | −0.0729682 | + | 0.126385i | ||||
\(381\) | 153.676 | − | 88.7250i | 0.403350 | − | 0.232874i | ||||
\(382\) | −175.430 | − | 303.854i | −0.459241 | − | 0.795428i | ||||
\(383\) | −413.753 | − | 238.881i | −1.08030 | − | 0.623709i | −0.149320 | − | 0.988789i | \(-0.547708\pi\) |
−0.930976 | + | 0.365080i | \(0.881042\pi\) | |||||||
\(384\) | − | 8.11689i | − | 0.0211377i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 218.267 | 0.565459 | ||||||||
\(387\) | 44.4853 | − | 77.0508i | 0.114949 | − | 0.199098i | ||||
\(388\) | 176.309 | − | 101.792i | 0.454404 | − | 0.262350i | ||||
\(389\) | −85.1102 | − | 147.415i | −0.218792 | − | 0.378959i | 0.735647 | − | 0.677365i | \(-0.236878\pi\) |
−0.954439 | + | 0.298406i | \(0.903545\pi\) | |||||||
\(390\) | 89.0955 | + | 51.4393i | 0.228450 | + | 0.131896i | ||||
\(391\) | − | 104.292i | − | 0.266732i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −105.926 | −0.269532 | ||||||||
\(394\) | 128.059 | − | 221.804i | 0.325023 | − | 0.562956i | ||||
\(395\) | 194.025 | − | 112.021i | 0.491204 | − | 0.283597i | ||||
\(396\) | 40.3675 | + | 69.9186i | 0.101938 | + | 0.176562i | ||||
\(397\) | −211.786 | − | 122.275i | −0.533467 | − | 0.307997i | 0.208960 | − | 0.977924i | \(-0.432992\pi\) |
−0.742427 | + | 0.669927i | \(0.766325\pi\) | |||||||
\(398\) | − | 493.146i | − | 1.23906i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −75.8823 | −0.189706 | ||||||||
\(401\) | 208.786 | − | 361.629i | 0.520664 | − | 0.901817i | −0.479047 | − | 0.877789i | \(-0.659018\pi\) |
0.999711 | − | 0.0240277i | \(-0.00764899\pi\) | |||||||
\(402\) | 30.4371 | − | 17.5729i | 0.0757142 | − | 0.0437136i | ||||
\(403\) | 373.617 | + | 647.124i | 0.927090 | + | 1.60577i | ||||
\(404\) | −103.368 | − | 59.6793i | −0.255860 | − | 0.147721i | ||||
\(405\) | − | 446.716i | − | 1.10300i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.9920 | 0.0343784 | ||||||||
\(408\) | −3.81623 | + | 6.60991i | −0.00935351 | + | 0.0162008i | ||||
\(409\) | −266.919 | + | 154.106i | −0.652614 | + | 0.376787i | −0.789457 | − | 0.613806i | \(-0.789638\pi\) |
0.136843 | + | 0.990593i | \(0.456304\pi\) | |||||||
\(410\) | 131.095 | + | 227.064i | 0.319745 | + | 0.553815i | ||||
\(411\) | −20.2386 | − | 11.6848i | −0.0492424 | − | 0.0284301i | ||||
\(412\) | 240.356i | 0.583388i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −332.735 | −0.803708 | ||||||||
\(415\) | 422.985 | − | 732.631i | 1.01924 | − | 1.76538i | ||||
\(416\) | 74.9117 | − | 43.2503i | 0.180076 | − | 0.103967i | ||||
\(417\) | −24.6030 | − | 42.6137i | −0.0590001 | − | 0.102191i | ||||
\(418\) | 24.3640 | + | 14.0665i | 0.0582870 | + | 0.0336520i | ||||
\(419\) | − | 103.142i | − | 0.246163i | −0.992397 | − | 0.123081i | \(-0.960722\pi\) | ||
0.992397 | − | 0.123081i | \(-0.0392776\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −165.220 | −0.392447 | −0.196224 | − | 0.980559i | \(-0.562868\pi\) | ||||
−0.196224 | + | 0.980559i | \(0.562868\pi\) | |||||||
\(422\) | −257.439 | + | 445.897i | −0.610044 | + | 1.05663i | ||||
\(423\) | 387.110 | − | 223.498i | 0.915153 | − | 0.528364i | ||||
\(424\) | −79.1543 | − | 137.099i | −0.186685 | − | 0.323347i | ||||
\(425\) | 61.7939 | + | 35.6767i | 0.145398 | + | 0.0839453i | ||||
\(426\) | − | 36.9587i | − | 0.0867574i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −227.220 | −0.530889 | ||||||||
\(429\) | 26.0955 | − | 45.1987i | 0.0608286 | − | 0.105358i | ||||
\(430\) | 85.1543 | − | 49.1639i | 0.198033 | − | 0.114335i | ||||
\(431\) | −297.268 | − | 514.883i | −0.689717 | − | 1.19463i | −0.971929 | − | 0.235273i | \(-0.924402\pi\) |
0.282212 | − | 0.959352i | \(-0.408932\pi\) | |||||||
\(432\) | 43.4558 | + | 25.0892i | 0.100592 | + | 0.0580770i | ||||
\(433\) | − | 40.6267i | − | 0.0938261i | −0.998899 | − | 0.0469131i | \(-0.985062\pi\) | ||
0.998899 | − | 0.0469131i | \(-0.0149384\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.7208 | −0.0384386 | ||||||||
\(436\) | 145.309 | − | 251.682i | 0.333277 | − | 0.577252i | ||||
\(437\) | −100.412 | + | 57.9727i | −0.229775 | + | 0.132661i | ||||
\(438\) | 26.6878 | + | 46.2246i | 0.0609310 | + | 0.105536i | ||||
\(439\) | −126.959 | − | 73.3001i | −0.289201 | − | 0.166971i | 0.348380 | − | 0.937353i | \(-0.386732\pi\) |
−0.637582 | + | 0.770383i | \(0.720065\pi\) | |||||||
\(440\) | 89.2261i | 0.202787i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −81.3381 | −0.184023 | ||||||||
\(443\) | −53.6802 | + | 92.9768i | −0.121174 | + | 0.209880i | −0.920231 | − | 0.391376i | \(-0.871999\pi\) |
0.799057 | + | 0.601256i | \(0.205333\pi\) | |||||||
\(444\) | 3.65476 | − | 2.11008i | 0.00823145 | − | 0.00475243i | ||||
\(445\) | 166.875 | + | 289.035i | 0.374999 | + | 0.649518i | ||||
\(446\) | −150.926 | − | 87.1372i | −0.338399 | − | 0.195375i | ||||
\(447\) | − | 66.2892i | − | 0.148298i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 135.161 | 0.301028 | 0.150514 | − | 0.988608i | \(-0.451907\pi\) | ||||
0.150514 | + | 0.988608i | \(0.451907\pi\) | |||||||
\(450\) | 113.823 | − | 197.148i | 0.252941 | − | 0.438106i | ||||
\(451\) | 115.191 | − | 66.5055i | 0.255412 | − | 0.147462i | ||||
\(452\) | −34.5442 | − | 59.8322i | −0.0764251 | − | 0.132372i | ||||
\(453\) | −57.0290 | − | 32.9257i | −0.125892 | − | 0.0726837i | ||||
\(454\) | 108.011i | 0.237910i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.48528 | 0.0186081 | ||||||||
\(457\) | −79.8675 | + | 138.335i | −0.174765 | + | 0.302702i | −0.940080 | − | 0.340954i | \(-0.889250\pi\) |
0.765315 | + | 0.643656i | \(0.222583\pi\) | |||||||
\(458\) | 437.584 | − | 252.639i | 0.955424 | − | 0.551614i | ||||
\(459\) | −23.5919 | − | 40.8623i | −0.0513984 | − | 0.0890247i | ||||
\(460\) | −318.463 | − | 183.865i | −0.692311 | − | 0.399706i | ||||
\(461\) | 310.250i | 0.672993i | 0.941685 | + | 0.336497i | \(0.109242\pi\) | ||||
−0.941685 | + | 0.336497i | \(0.890758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −326.014 | −0.704135 | −0.352067 | − | 0.935975i | \(-0.614521\pi\) | ||||
−0.352067 | + | 0.935975i | \(0.614521\pi\) | |||||||
\(464\) | −7.02944 | + | 12.1753i | −0.0151496 | + | 0.0262400i | ||||
\(465\) | −201.331 | + | 116.238i | −0.432969 | + | 0.249975i | ||||
\(466\) | 193.092 | + | 334.445i | 0.414360 | + | 0.717693i | ||||
\(467\) | −515.769 | − | 297.779i | −1.10443 | − | 0.637643i | −0.167048 | − | 0.985949i | \(-0.553424\pi\) |
−0.937381 | + | 0.348306i | \(0.886757\pi\) | |||||||
\(468\) | 259.502i | 0.554491i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 494.007 | 1.05108 | ||||||||
\(471\) | 3.03344 | − | 5.25408i | 0.00644043 | − | 0.0111551i | ||||
\(472\) | −94.8457 | + | 54.7592i | −0.200944 | + | 0.116015i | ||||
\(473\) | −24.9411 | − | 43.1993i | −0.0527297 | − | 0.0913304i | ||||
\(474\) | −29.6878 | − | 17.1402i | −0.0626324 | − | 0.0361608i | ||||
\(475\) | − | 79.3262i | − | 0.167002i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 474.926 | 0.995652 | ||||||||
\(478\) | 187.456 | − | 324.683i | 0.392167 | − | 0.679253i | ||||
\(479\) | −438.798 | + | 253.340i | −0.916071 | + | 0.528894i | −0.882379 | − | 0.470539i | \(-0.844060\pi\) |
−0.0336914 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(480\) | 13.4558 | + | 23.3062i | 0.0280330 | + | 0.0485546i | ||||
\(481\) | 38.9483 | + | 22.4868i | 0.0809735 | + | 0.0467501i | ||||
\(482\) | 123.939i | 0.257135i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −196.735 | −0.406477 | ||||||||
\(485\) | −337.492 | + | 584.554i | −0.695861 | + | 1.20527i | ||||
\(486\) | −197.470 | + | 114.009i | −0.406317 | + | 0.234587i | ||||
\(487\) | −105.651 | − | 182.992i | −0.216942 | − | 0.375755i | 0.736930 | − | 0.675970i | \(-0.236275\pi\) |
−0.953872 | + | 0.300215i | \(0.902942\pi\) | |||||||
\(488\) | 221.698 | + | 127.998i | 0.454300 | + | 0.262290i | ||||
\(489\) | − | 159.255i | − | 0.325676i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −784.161 | −1.59707 | −0.798534 | − | 0.601949i | \(-0.794391\pi\) | ||||
−0.798534 | + | 0.601949i | \(0.794391\pi\) | |||||||
\(492\) | 20.0589 | − | 34.7430i | 0.0407701 | − | 0.0706158i | ||||
\(493\) | 11.4487 | − | 6.60991i | 0.0232225 | − | 0.0134075i | ||||
\(494\) | 45.2132 | + | 78.3116i | 0.0915247 | + | 0.158525i | ||||
\(495\) | −231.816 | − | 133.839i | −0.468316 | − | 0.270382i | ||||
\(496\) | 195.467i | 0.394086i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −129.442 | −0.259923 | ||||||||
\(499\) | 85.7462 | − | 148.517i | 0.171836 | − | 0.297629i | −0.767226 | − | 0.641377i | \(-0.778363\pi\) |
0.939062 | + | 0.343748i | \(0.111697\pi\) | |||||||
\(500\) | −69.2498 | + | 39.9814i | −0.138500 | + | 0.0799628i | ||||
\(501\) | −60.5665 | − | 104.904i | −0.120891 | − | 0.209390i | ||||
\(502\) | 607.051 | + | 350.481i | 1.20926 | + | 0.698169i | ||||
\(503\) | − | 20.0883i | − | 0.0399370i | −0.999801 | − | 0.0199685i | \(-0.993643\pi\) | ||
0.999801 | − | 0.0199685i | \(-0.00635659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 395.735 | 0.783634 | ||||||||
\(506\) | −93.2756 | + | 161.558i | −0.184339 | + | 0.319285i | ||||
\(507\) | 40.2761 | − | 23.2534i | 0.0794400 | − | 0.0458647i | ||||
\(508\) | 247.338 | + | 428.402i | 0.486886 | + | 0.843311i | ||||
\(509\) | 412.890 | + | 238.382i | 0.811178 | + | 0.468334i | 0.847365 | − | 0.531011i | \(-0.178188\pi\) |
−0.0361865 | + | 0.999345i | \(0.511521\pi\) | |||||||
\(510\) | − | 25.3056i | − | 0.0496187i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −26.2279 | + | 45.4281i | −0.0511266 | + | 0.0885538i | ||||
\(514\) | 490.555 | − | 283.222i | 0.954387 | − | 0.551016i | ||||
\(515\) | −398.452 | − | 690.139i | −0.773693 | − | 1.34008i | ||||
\(516\) | −13.0294 | − | 7.52255i | −0.0252508 | − | 0.0145786i | ||||
\(517\) | − | 250.613i | − | 0.484744i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −117.905 | −0.227176 | ||||||||
\(520\) | −143.397 | + | 248.371i | −0.275763 | + | 0.477636i | ||||
\(521\) | −739.823 | + | 427.137i | −1.42001 | + | 0.819841i | −0.996299 | − | 0.0859587i | \(-0.972605\pi\) |
−0.423707 | + | 0.905799i | \(0.639271\pi\) | |||||||
\(522\) | −21.0883 | − | 36.5260i | −0.0403991 | − | 0.0699732i | ||||
\(523\) | 513.554 | + | 296.501i | 0.981940 | + | 0.566923i | 0.902855 | − | 0.429945i | \(-0.141467\pi\) |
0.0790845 | + | 0.996868i | \(0.474800\pi\) | |||||||
\(524\) | − | 295.289i | − | 0.563529i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −45.7431 | −0.0869640 | ||||||||
\(527\) | 91.9005 | − | 159.176i | 0.174384 | − | 0.302043i | ||||
\(528\) | 11.8234 | − | 6.82623i | 0.0223928 | − | 0.0129285i | ||||
\(529\) | −119.919 | − | 207.706i | −0.226690 | − | 0.392638i | ||||
\(530\) | 454.555 | + | 262.437i | 0.857651 | + | 0.495165i | ||||
\(531\) | − | 328.555i | − | 0.618748i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 427.529 | 0.802118 | ||||||||
\(534\) | 25.5334 | − | 44.2252i | 0.0478154 | − | 0.0828188i | ||||
\(535\) | 652.422 | − | 376.676i | 1.21948 | − | 0.704068i | ||||
\(536\) | 48.9878 | + | 84.8494i | 0.0913952 | + | 0.158301i | ||||
\(537\) | 115.058 | + | 66.4290i | 0.214262 | + | 0.123704i | ||||
\(538\) | 434.112i | 0.806899i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −166.368 | −0.308088 | ||||||||
\(541\) | −427.595 | + | 740.617i | −0.790380 | + | 1.36898i | 0.135352 | + | 0.990798i | \(0.456783\pi\) |
−0.925732 | + | 0.378180i | \(0.876550\pi\) | |||||||
\(542\) | −93.0624 | + | 53.7296i | −0.171702 | + | 0.0991322i | ||||
\(543\) | 55.6325 | + | 96.3583i | 0.102454 | + | 0.177455i | ||||
\(544\) | −18.4264 | − | 10.6385i | −0.0338721 | − | 0.0195560i | ||||
\(545\) | 963.546i | 1.76797i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 415.897 | 0.760323 | 0.380161 | − | 0.924920i | \(-0.375868\pi\) | ||||
0.380161 | + | 0.924920i | \(0.375868\pi\) | |||||||
\(548\) | 32.5736 | − | 56.4191i | 0.0594409 | − | 0.102955i | ||||
\(549\) | −665.095 | + | 383.993i | −1.21147 | + | 0.699441i | ||||
\(550\) | −63.8162 | − | 110.533i | −0.116030 | − | 0.200969i | ||||
\(551\) | −12.7279 | − | 7.34847i | −0.0230997 | − | 0.0133366i | ||||
\(552\) | 56.2662i | 0.101931i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 393.733 | 0.710709 | ||||||||
\(555\) | −6.99600 | + | 12.1174i | −0.0126054 | + | 0.0218332i | ||||
\(556\) | 118.794 | − | 68.5857i | 0.213658 | − | 0.123356i | ||||
\(557\) | 292.110 | + | 505.950i | 0.524435 | + | 0.908348i | 0.999595 | + | 0.0284485i | \(0.00905667\pi\) |
−0.475160 | + | 0.879899i | \(0.657610\pi\) | |||||||
\(558\) | −507.838 | − | 293.200i | −0.910103 | − | 0.525448i | ||||
\(559\) | − | 160.333i | − | 0.286822i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.8377 | −0.0228835 | ||||||||
\(562\) | −279.088 | + | 483.395i | −0.496598 | + | 0.860134i | ||||
\(563\) | −789.076 | + | 455.573i | −1.40156 | + | 0.809189i | −0.994552 | − | 0.104237i | \(-0.966760\pi\) |
−0.407004 | + | 0.913426i | \(0.633427\pi\) | |||||||
\(564\) | −37.7939 | − | 65.4610i | −0.0670105 | − | 0.116066i | ||||
\(565\) | 198.375 | + | 114.532i | 0.351106 | + | 0.202711i | ||||
\(566\) | − | 207.035i | − | 0.365787i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 103.029 | 0.181390 | ||||||||
\(569\) | −350.000 | + | 606.217i | −0.615113 | + | 1.06541i | 0.375251 | + | 0.926923i | \(0.377556\pi\) |
−0.990365 | + | 0.138485i | \(0.955777\pi\) | |||||||
\(570\) | −24.3640 | + | 14.0665i | −0.0427438 | + | 0.0246781i | ||||
\(571\) | 281.231 | + | 487.107i | 0.492525 | + | 0.853077i | 0.999963 | − | 0.00861055i | \(-0.00274086\pi\) |
−0.507438 | + | 0.861688i | \(0.669408\pi\) | |||||||
\(572\) | 126.000 | + | 72.7461i | 0.220280 | + | 0.127179i | ||||
\(573\) | − | 177.993i | − | 0.310634i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 526.014 | 0.914807 | ||||||||
\(576\) | −33.9411 | + | 58.7878i | −0.0589256 | + | 0.102062i | ||||
\(577\) | 573.014 | − | 330.830i | 0.993092 | − | 0.573362i | 0.0868946 | − | 0.996218i | \(-0.472306\pi\) |
0.906197 | + | 0.422856i | \(0.138972\pi\) | |||||||
\(578\) | −194.350 | − | 336.625i | −0.336246 | − | 0.582395i | ||||
\(579\) | 95.8934 | + | 55.3641i | 0.165619 | + | 0.0956202i | ||||
\(580\) | − | 46.6124i | − | 0.0803662i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 103.279 | 0.177456 | ||||||||
\(583\) | 133.136 | − | 230.598i | 0.228364 | − | 0.395538i | ||||
\(584\) | −128.860 | + | 74.3973i | −0.220651 | + | 0.127393i | ||||
\(585\) | −430.191 | − | 745.113i | −0.735369 | − | 1.27370i | ||||
\(586\) | −367.029 | − | 211.905i | −0.626330 | − | 0.361612i | ||||
\(587\) | − | 823.029i | − | 1.40209i | −0.713116 | − | 0.701046i | \(-0.752717\pi\) | ||
0.713116 | − | 0.701046i | \(-0.247283\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −204.338 | −0.346924 | ||||||||
\(590\) | 181.555 | − | 314.462i | 0.307720 | − | 0.532987i | ||||
\(591\) | 112.523 | − | 64.9650i | 0.190394 | − | 0.109924i | ||||
\(592\) | 5.88225 | + | 10.1884i | 0.00993623 | + | 0.0172101i | ||||
\(593\) | 538.890 | + | 311.128i | 0.908752 | + | 0.524668i | 0.880029 | − | 0.474919i | \(-0.157523\pi\) |
0.0287225 | + | 0.999587i | \(0.490856\pi\) | |||||||
\(594\) | 84.3992i | 0.142086i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 184.794 | 0.310057 | ||||||||
\(597\) | 125.088 | − | 216.659i | 0.209527 | − | 0.362912i | ||||
\(598\) | −519.286 | + | 299.810i | −0.868372 | + | 0.501355i | ||||
\(599\) | 256.422 | + | 444.137i | 0.428084 | + | 0.741463i | 0.996703 | − | 0.0811377i | \(-0.0258554\pi\) |
−0.568619 | + | 0.822601i | \(0.692522\pi\) | |||||||
\(600\) | −33.3381 | − | 19.2478i | −0.0555635 | − | 0.0320796i | ||||
\(601\) | 680.160i | 1.13171i | 0.824504 | + | 0.565857i | \(0.191454\pi\) | ||||
−0.824504 | + | 0.565857i | \(0.808546\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −293.927 | −0.487441 | ||||||||
\(604\) | 91.7868 | − | 158.979i | 0.151965 | − | 0.263211i | ||||
\(605\) | 564.889 | − | 326.139i | 0.933701 | − | 0.539073i | ||||
\(606\) | −30.2756 | − | 52.4390i | −0.0499598 | − | 0.0865329i | ||||
\(607\) | −33.5482 | − | 19.3690i | −0.0552688 | − | 0.0319095i | 0.472111 | − | 0.881539i | \(-0.343492\pi\) |
−0.527380 | + | 0.849630i | \(0.676825\pi\) | |||||||
\(608\) | 23.6544i | 0.0389052i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −848.756 | −1.39140 | ||||||||
\(611\) | 402.765 | − | 697.609i | 0.659189 | − | 1.14175i | ||||
\(612\) | 55.2792 | − | 31.9155i | 0.0903255 | − | 0.0521495i | ||||
\(613\) | −200.552 | − | 347.366i | −0.327164 | − | 0.566665i | 0.654784 | − | 0.755816i | \(-0.272760\pi\) |
−0.981948 | + | 0.189151i | \(0.939426\pi\) | |||||||
\(614\) | 25.7056 | + | 14.8412i | 0.0418658 | + | 0.0241713i | ||||
\(615\) | 133.011i | 0.216278i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −959.044 | −1.55437 | −0.777183 | − | 0.629275i | \(-0.783352\pi\) | ||||
−0.777183 | + | 0.629275i | \(0.783352\pi\) | |||||||
\(618\) | −60.9670 | + | 105.598i | −0.0986521 | + | 0.170870i | ||||
\(619\) | 869.951 | − | 502.267i | 1.40541 | − | 0.811416i | 0.410473 | − | 0.911873i | \(-0.365364\pi\) |
0.994941 | + | 0.100457i | \(0.0320303\pi\) | |||||||
\(620\) | −324.037 | − | 561.248i | −0.522640 | − | 0.905238i | ||||
\(621\) | −301.235 | − | 173.918i | −0.485081 | − | 0.280061i | ||||
\(622\) | − | 257.443i | − | 0.413895i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 43.8823 | 0.0703241 | ||||||||
\(625\) | 369.691 | − | 640.323i | 0.591505 | − | 1.02452i | ||||
\(626\) | −119.938 | + | 69.2460i | −0.191594 | + | 0.110617i | ||||
\(627\) | 7.13604 | + | 12.3600i | 0.0113812 | + | 0.0197129i | ||||
\(628\) | 14.6468 | + | 8.45631i | 0.0233229 | + | 0.0134655i | ||||
\(629\) | − | 11.0624i | − | 0.0175873i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −386.514 | −0.612542 | −0.306271 | − | 0.951944i | \(-0.599081\pi\) | ||||
−0.306271 | + | 0.951944i | \(0.599081\pi\) | |||||||
\(632\) | 47.7817 | − | 82.7604i | 0.0756040 | − | 0.130950i | ||||
\(633\) | −226.206 | + | 130.600i | −0.357356 | + | 0.206319i | ||||
\(634\) | 340.805 | + | 590.291i | 0.537547 | + | 0.931058i | ||||
\(635\) | −1420.37 | − | 820.053i | −2.23681 | − | 1.29142i | ||||
\(636\) | − | 80.3109i | − | 0.126275i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −23.6468 | −0.0370639 | ||||||||
\(639\) | −154.544 | + | 267.678i | −0.241853 | + | 0.418902i | ||||
\(640\) | −64.9706 | + | 37.5108i | −0.101517 | + | 0.0586106i | ||||
\(641\) | 496.074 | + | 859.225i | 0.773906 | + | 1.34044i | 0.935407 | + | 0.353572i | \(0.115033\pi\) |
−0.161502 | + | 0.986872i | \(0.551634\pi\) | |||||||
\(642\) | −99.8269 | − | 57.6351i | −0.155494 | − | 0.0897743i | ||||
\(643\) | 944.986i | 1.46965i | 0.678256 | + | 0.734826i | \(0.262736\pi\) | ||||
−0.678256 | + | 0.734826i | \(0.737264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.8823 | 0.0773368 | ||||||||
\(646\) | 11.1213 | − | 19.2627i | 0.0172157 | − | 0.0298184i | ||||
\(647\) | −2.50357 | + | 1.44544i | −0.00386951 | + | 0.00223406i | −0.501934 | − | 0.864906i | \(-0.667378\pi\) |
0.498064 | + | 0.867140i | \(0.334044\pi\) | |||||||
\(648\) | −95.2721 | − | 165.016i | −0.147025 | − | 0.254654i | ||||
\(649\) | −159.529 | − | 92.1039i | −0.245807 | − | 0.141917i | ||||
\(650\) | − | 410.241i | − | 0.631140i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 443.955 | 0.680913 | ||||||||
\(653\) | 161.529 | − | 279.777i | 0.247365 | − | 0.428449i | −0.715429 | − | 0.698686i | \(-0.753769\pi\) |
0.962794 | + | 0.270237i | \(0.0871019\pi\) | |||||||
\(654\) | 127.680 | − | 73.7159i | 0.195229 | − | 0.112716i | ||||
\(655\) | 489.518 | + | 847.870i | 0.747356 | + | 1.29446i | ||||
\(656\) | 96.8528 | + | 55.9180i | 0.147641 | + | 0.0852409i | ||||
\(657\) | − | 446.384i | − | 0.679428i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 295.955 | 0.449098 | 0.224549 | − | 0.974463i | \(-0.427909\pi\) | ||||
0.224549 | + | 0.974463i | \(0.427909\pi\) | |||||||
\(660\) | −22.6325 | + | 39.2006i | −0.0342916 | + | 0.0593948i | ||||
\(661\) | −17.9710 | + | 10.3756i | −0.0271876 | + | 0.0156968i | −0.513532 | − | 0.858070i | \(-0.671663\pi\) |
0.486345 | + | 0.873767i | \(0.338330\pi\) | |||||||
\(662\) | −159.104 | − | 275.576i | −0.240338 | − | 0.416278i | ||||
\(663\) | −35.7351 | − | 20.6316i | −0.0538990 | − | 0.0311186i | ||||
\(664\) | − | 360.843i | − | 0.543439i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −35.2935 | −0.0529933 | ||||||||
\(667\) | 48.7279 | − | 84.3992i | 0.0730554 | − | 0.126536i | ||||
\(668\) | 292.441 | − | 168.841i | 0.437785 | − | 0.252756i | ||||
\(669\) | −44.2052 | − | 76.5656i | −0.0660765 | − | 0.114448i | ||||
\(670\) | −281.319 | − | 162.420i | −0.419880 | − | 0.242418i | ||||
\(671\) | 430.579i | 0.641698i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 627.044 | 0.931714 | 0.465857 | − | 0.884860i | \(-0.345746\pi\) | ||||
0.465857 | + | 0.884860i | \(0.345746\pi\) | |||||||
\(674\) | 186.936 | − | 323.783i | 0.277353 | − | 0.480390i | ||||
\(675\) | 206.095 | − | 118.989i | 0.305327 | − | 0.176280i | ||||
\(676\) | 64.8234 | + | 112.277i | 0.0958926 | + | 0.166091i | ||||
\(677\) | 94.6097 | + | 54.6230i | 0.139749 | + | 0.0806838i | 0.568244 | − | 0.822860i | \(-0.307623\pi\) |
−0.428496 | + | 0.903544i | \(0.640956\pi\) | |||||||
\(678\) | − | 35.0489i | − | 0.0516946i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 70.5442 | 0.103741 | ||||||||
\(681\) | −27.3974 | + | 47.4537i | −0.0402311 | + | 0.0696824i | ||||
\(682\) | −284.724 | + | 164.386i | −0.417484 | + | 0.241035i | ||||
\(683\) | −396.783 | − | 687.248i | −0.580941 | − | 1.00622i | −0.995368 | − | 0.0961370i | \(-0.969351\pi\) |
0.414427 | − | 0.910083i | \(-0.363982\pi\) | |||||||
\(684\) | −61.4558 | − | 35.4815i | −0.0898477 | − | 0.0518736i | ||||
\(685\) | 215.996i | 0.315323i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 256.331 | 0.373116 | ||||||||
\(688\) | 20.9706 | − | 36.3221i | 0.0304805 | − | 0.0527937i | ||||
\(689\) | 741.198 | − | 427.931i | 1.07576 | − | 0.621090i | ||||
\(690\) | −93.2756 | − | 161.558i | −0.135182 | − | 0.234142i | ||||
\(691\) | −159.253 | − | 91.9447i | −0.230467 | − | 0.133060i | 0.380320 | − | 0.924855i | \(-0.375814\pi\) |
−0.610788 | + | 0.791794i | \(0.709147\pi\) | |||||||
\(692\) | − | 328.682i | − | 0.474974i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −270.478 | −0.389738 | ||||||||
\(695\) | −227.397 | + | 393.863i | −0.327190 | + | 0.566710i | ||||
\(696\) | −6.17662 | + | 3.56608i | −0.00887446 | + | 0.00512367i | ||||
\(697\) | −52.5807 | − | 91.0725i | −0.0754386 | − | 0.130664i | ||||
\(698\) | −165.889 | − | 95.7763i | −0.237664 | − | 0.137215i | ||||
\(699\) | 195.913i | 0.280277i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1043.82 | −1.48905 | −0.744525 | − | 0.667595i | \(-0.767324\pi\) | ||||
−0.744525 | + | 0.667595i | \(0.767324\pi\) | |||||||
\(702\) | −135.640 | + | 234.935i | −0.193219 | + | 0.334665i | ||||
\(703\) | −10.6508 | + | 6.14922i | −0.0151504 | + | 0.00874711i | ||||
\(704\) | 19.0294 | + | 32.9600i | 0.0270305 | + | 0.0468181i | ||||
\(705\) | 217.037 | + | 125.306i | 0.307854 | + | 0.177740i | ||||
\(706\) | 492.840i | 0.698073i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −55.5593 | −0.0784736 | ||||||||
\(709\) | 490.279 | − | 849.188i | 0.691507 | − | 1.19773i | −0.279836 | − | 0.960048i | \(-0.590280\pi\) |
0.971344 | − | 0.237678i | \(-0.0763864\pi\) | |||||||
\(710\) | −295.831 | + | 170.798i | −0.416663 | + | 0.240560i | ||||
\(711\) | 143.345 | + | 248.281i | 0.201611 | + | 0.349200i | ||||
\(712\) | 123.286 | + | 71.1794i | 0.173155 | + | 0.0999711i | ||||
\(713\) | − | 1354.97i | − | 1.90038i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −482.382 | −0.674660 | ||||||||
\(716\) | −185.184 | + | 320.748i | −0.258637 | + | 0.447972i | ||||
\(717\) | 164.714 | − | 95.0975i | 0.229726 | − | 0.132632i | ||||
\(718\) | −215.548 | − | 373.340i | −0.300206 | − | 0.519972i | ||||
\(719\) | 674.187 | + | 389.242i | 0.937673 | + | 0.541366i | 0.889230 | − | 0.457460i | \(-0.151241\pi\) |
0.0484429 | + | 0.998826i | \(0.484574\pi\) | |||||||
\(720\) | − | 225.065i | − | 0.312590i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 485.803 | 0.672858 | ||||||||
\(723\) | −31.4376 | + | 54.4514i | −0.0434821 | + | 0.0753132i | ||||
\(724\) | −268.617 | + | 155.086i | −0.371018 | + | 0.214208i | ||||
\(725\) | 33.3381 | + | 57.7433i | 0.0459836 | + | 0.0796459i | ||||
\(726\) | −86.4335 | − | 49.9024i | −0.119054 | − | 0.0687361i | ||||
\(727\) | − | 735.255i | − | 1.01135i | −0.862723 | − | 0.505677i | \(-0.831243\pi\) | ||
0.862723 | − | 0.505677i | \(-0.168757\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 490.632 | 0.673021 | ||||||||
\(730\) | 246.665 | − | 427.237i | 0.337898 | − | 0.585256i | ||||
\(731\) | −34.1543 | + | 19.7190i | −0.0467227 | + | 0.0269754i | ||||
\(732\) | 64.9340 | + | 112.469i | 0.0887076 | + | 0.153646i | ||||
\(733\) | 414.705 | + | 239.430i | 0.565764 | + | 0.326644i | 0.755456 | − | 0.655200i | \(-0.227415\pi\) |
−0.189692 | + | 0.981844i | \(0.560749\pi\) | |||||||
\(734\) | 134.356i | 0.183047i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −156.853 | −0.213115 | ||||||||
\(737\) | −82.3965 | + | 142.715i | −0.111800 | + | 0.193643i | ||||
\(738\) | −290.558 | + | 167.754i | −0.393711 | + | 0.227309i | ||||
\(739\) | 9.95227 | + | 17.2378i | 0.0134672 | + | 0.0233259i | 0.872680 | − | 0.488292i | \(-0.162380\pi\) |
−0.859213 | + | 0.511618i | \(0.829046\pi\) | |||||||
\(740\) | −33.7797 | − | 19.5027i | −0.0456482 | − | 0.0263550i | ||||
\(741\) | 45.8739i | 0.0619080i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.3095 | 0.0582901 | 0.0291450 | − | 0.999575i | \(-0.490722\pi\) | ||||
0.0291450 | + | 0.999575i | \(0.490722\pi\) | |||||||
\(744\) | −49.5807 | + | 85.8764i | −0.0666408 | + | 0.115425i | ||||
\(745\) | −530.603 | + | 306.344i | −0.712218 | + | 0.411199i | ||||
\(746\) | −179.293 | − | 310.544i | −0.240339 | − | 0.416279i | ||||
\(747\) | 937.499 | + | 541.265i | 1.25502 | + | 0.724585i | ||||
\(748\) | − | 35.7875i | − | 0.0478442i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −40.5656 | −0.0540874 | ||||||||
\(751\) | −112.665 | + | 195.142i | −0.150020 | + | 0.259842i | −0.931235 | − | 0.364420i | \(-0.881267\pi\) |
0.781215 | + | 0.624263i | \(0.214600\pi\) | |||||||
\(752\) | 182.485 | − | 105.358i | 0.242667 | − | 0.140104i | ||||
\(753\) | 177.801 | + | 307.961i | 0.236124 | + | 0.408978i | ||||
\(754\) | −65.8234 | − | 38.0031i | −0.0872989 | − | 0.0504020i | ||||
\(755\) | 608.641i | 0.806147i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 935.779 | 1.23617 | 0.618084 | − | 0.786112i | \(-0.287909\pi\) | ||||
0.618084 | + | 0.786112i | \(0.287909\pi\) | |||||||
\(758\) | −359.387 | + | 622.476i | −0.474125 | + | 0.821209i | ||||
\(759\) | −81.9594 | + | 47.3193i | −0.107983 | + | 0.0623443i | ||||
\(760\) | −39.2132 | − | 67.9193i | −0.0515963 | − | 0.0893674i | ||||
\(761\) | −1214.79 | − | 701.357i | −1.59630 | − | 0.921625i | −0.992191 | − | 0.124724i | \(-0.960195\pi\) |
−0.604110 | − | 0.796901i | \(-0.706471\pi\) | |||||||
\(762\) | 250.952i | 0.329334i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 496.191 | 0.649465 | ||||||||
\(765\) | −105.816 | + | 183.279i | −0.138322 | + | 0.239581i | ||||
\(766\) | 585.136 | − | 337.828i | 0.763885 | − | 0.441029i | ||||
\(767\) | −296.044 | − | 512.763i | −0.385976 | − | 0.668530i | ||||
\(768\) | 9.94113 | + | 5.73951i | 0.0129442 | + | 0.00747332i | ||||
\(769\) | 1.72330i | 0.00224097i | 0.999999 | + | 0.00112048i | \(0.000356661\pi\) | ||||
−0.999999 | + | 0.00112048i | \(0.999643\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 287.360 | 0.372711 | ||||||||
\(772\) | −154.338 | + | 267.321i | −0.199920 | + | 0.346271i | ||||
\(773\) | −194.213 | + | 112.129i | −0.251245 | + | 0.145057i | −0.620334 | − | 0.784337i | \(-0.713003\pi\) |
0.369089 | + | 0.929394i | \(0.379670\pi\) | |||||||
\(774\) | 62.9117 | + | 108.966i | 0.0812813 | + | 0.140783i | ||||
\(775\) | 802.831 | + | 463.514i | 1.03591 | + | 0.598083i | ||||
\(776\) | 287.911i | 0.371019i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 240.728 | 0.309419 | ||||||||
\(779\) | −58.4558 | + | 101.248i | −0.0750396 | + | 0.129972i | ||||
\(780\) | −126.000 | + | 72.7461i | −0.161538 | + | 0.0932643i | ||||
\(781\) | 86.6468 | + | 150.077i | 0.110943 | + | 0.192160i | ||||
\(782\) | 127.731 | + | 73.7458i | 0.163340 | + | 0.0943041i | ||||
\(783\) | − | 44.0908i | − | 0.0563101i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −56.0740 | −0.0714319 | ||||||||
\(786\) | 74.9010 | − | 129.732i | 0.0952939 | − | 0.165054i | ||||
\(787\) | −60.7979 | + | 35.1017i | −0.0772528 | + | 0.0446019i | −0.538129 | − | 0.842863i | \(-0.680869\pi\) |
0.460876 | + | 0.887465i | \(0.347535\pi\) | |||||||
\(788\) | 181.103 | + | 313.679i | 0.229826 | + | 0.398070i | ||||
\(789\) | −20.0968 | − | 11.6029i | −0.0254712 | − | 0.0147058i | ||||
\(790\) | 316.842i | 0.401066i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −114.177 | −0.144162 | ||||||||
\(793\) | −691.992 | + | 1198.57i | −0.872625 | + | 1.51143i | ||||
\(794\) | 299.511 | − | 172.923i | 0.377218 | − | 0.217787i | ||||
\(795\) | 133.136 | + | 230.598i | 0.167467 | + | 0.290061i | ||||
\(796\) | 603.978 | + | 348.707i | 0.758766 | + | 0.438074i | ||||
\(797\) | 1305.38i | 1.63787i | 0.573889 | + | 0.818933i | \(0.305434\pi\) | ||||
−0.573889 | + | 0.818933i | \(0.694566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −198.140 | −0.247985 | ||||||||
\(800\) | 53.6569 | − | 92.9364i | 0.0670711 | − | 0.116170i | ||||
\(801\) | −369.859 | + | 213.538i | −0.461747 | + | 0.266590i | ||||
\(802\) | 295.269 | + | 511.420i | 0.368165 | + | 0.637681i | ||||
\(803\) | −216.740 | − | 125.135i | −0.269913 | − | 0.155834i | ||||
\(804\) | 49.7036i | 0.0618204i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1056.75 | −1.31110 | ||||||||
\(807\) | −110.114 | + | 190.723i | −0.136448 | + | 0.236335i | ||||
\(808\) | 146.184 | − | 84.3992i | 0.180921 | − | 0.104455i | ||||
\(809\) | −381.382 | − | 660.573i | −0.471424 | − | 0.816531i | 0.528041 | − | 0.849219i | \(-0.322927\pi\) |
−0.999466 | + | 0.0326879i | \(0.989593\pi\) | |||||||
\(810\) | 547.113 | + | 315.876i | 0.675449 | + | 0.389970i | ||||
\(811\) | 1214.98i | 1.49813i | 0.662498 | + | 0.749064i | \(0.269496\pi\) | ||||
−0.662498 | + | 0.749064i | \(0.730504\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −54.5147 | −0.0670538 | ||||||||
\(814\) | −9.89383 | + | 17.1366i | −0.0121546 | + | 0.0210524i | ||||
\(815\) | −1274.74 | + | 735.970i | −1.56410 | + | 0.903031i | ||||
\(816\) | −5.39697 | − | 9.34783i | −0.00661393 | − | 0.0114557i | ||||
\(817\) | 37.9706 | + | 21.9223i | 0.0464756 | + | 0.0268327i | ||||
\(818\) | − | 435.877i | − | 0.532857i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −370.794 | −0.452188 | ||||||||
\(821\) | 291.684 | − | 505.211i | 0.355279 | − | 0.615361i | −0.631887 | − | 0.775061i | \(-0.717719\pi\) |
0.987166 | + | 0.159700i | \(0.0510527\pi\) | |||||||
\(822\) | 28.6218 | − | 16.5248i | 0.0348197 | − | 0.0201031i | ||||
\(823\) | −515.371 | − | 892.648i | −0.626210 | − | 1.08463i | −0.988306 | − | 0.152486i | \(-0.951272\pi\) |
0.362096 | − | 0.932141i | \(-0.382061\pi\) | |||||||
\(824\) | −294.375 | − | 169.957i | −0.357251 | − | 0.206259i | ||||
\(825\) | − | 64.7487i | − | 0.0784833i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 152.102 | 0.183920 | 0.0919599 | − | 0.995763i | \(-0.470687\pi\) | ||||
0.0919599 | + | 0.995763i | \(0.470687\pi\) | |||||||
\(828\) | 235.279 | − | 407.516i | 0.284154 | − | 0.492169i | ||||
\(829\) | −532.095 | + | 307.205i | −0.641852 | + | 0.370573i | −0.785327 | − | 0.619081i | \(-0.787505\pi\) |
0.143476 | + | 0.989654i | \(0.454172\pi\) | |||||||
\(830\) | 598.191 | + | 1036.10i | 0.720712 | + | 1.24831i | ||||
\(831\) | 172.983 | + | 99.8715i | 0.208162 | + | 0.120182i | ||||
\(832\) | 122.330i | 0.147032i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 69.5879 | 0.0834387 | ||||||||
\(835\) | −559.794 | + | 969.592i | −0.670412 | + | 1.16119i | ||||
\(836\) | −34.4558 | + | 19.8931i | −0.0412151 | + | 0.0237956i | ||||
\(837\) | −306.507 | − | 530.886i | −0.366197 | − | 0.634272i | ||||
\(838\) | 126.323 | + | 72.9326i | 0.150743 | + | 0.0870317i | ||||
\(839\) | − | 1546.14i | − | 1.84284i | −0.388568 | − | 0.921420i | \(-0.627030\pi\) | ||
0.388568 | − | 0.921420i | \(-0.372970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −828.647 | −0.985311 | ||||||||
\(842\) | 116.828 | − | 202.353i | 0.138751 | − | 0.240324i | ||||
\(843\) | −245.229 | + | 141.583i | −0.290901 | + | 0.167952i | ||||
\(844\) | −364.073 | − | 630.593i | −0.431366 | − | 0.747148i | ||||
\(845\) | −372.257 | − | 214.923i | −0.440541 | − | 0.254347i | ||||
\(846\) | 632.148i | 0.747219i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 223.882 | 0.264012 | ||||||||
\(849\) | 52.5152 | − | 90.9589i | 0.0618553 | − | 0.107137i | ||||
\(850\) | −87.3898 | + | 50.4545i | −0.102812 | + | 0.0593583i | ||||
\(851\) | −40.7756 | − | 70.6255i | −0.0479150 | − | 0.0829912i | ||||
\(852\) | 45.2649 | + | 26.1337i | 0.0531279 | + | 0.0306734i | ||||
\(853\) | − | 1235.15i | − | 1.44800i | −0.689798 | − | 0.724002i | \(-0.742301\pi\) | ||
0.689798 | − | 0.724002i | \(-0.257699\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 235.279 | 0.275180 | ||||||||
\(856\) | 160.669 | − | 278.287i | 0.187697 | − | 0.325102i | ||||
\(857\) | 953.219 | − | 550.341i | 1.11227 | − | 0.642172i | 0.172857 | − | 0.984947i | \(-0.444700\pi\) |
0.939417 | + | 0.342775i | \(0.111367\pi\) | |||||||
\(858\) | 36.9045 | + | 63.9205i | 0.0430123 | + | 0.0744995i | ||||
\(859\) | −512.488 | − | 295.885i | −0.596610 | − | 0.344453i | 0.171096 | − | 0.985254i | \(-0.445269\pi\) |
−0.767707 | + | 0.640801i | \(0.778602\pi\) | |||||||
\(860\) | 139.056i | 0.161694i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 840.801 | 0.975407 | ||||||||
\(863\) | 32.3635 | − | 56.0553i | 0.0375012 | − | 0.0649540i | −0.846666 | − | 0.532125i | \(-0.821394\pi\) |
0.884167 | + | 0.467171i | \(0.154727\pi\) | |||||||
\(864\) | −61.4558 | + | 35.4815i | −0.0711294 | + | 0.0410666i | ||||
\(865\) | 544.875 | + | 943.751i | 0.629913 | + | 1.09104i | ||||
\(866\) | 49.7574 | + | 28.7274i | 0.0574565 | + | 0.0331725i | ||||
\(867\) | − | 197.190i | − | 0.227440i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 160.736 | 0.184967 | ||||||||
\(870\) | 11.8234 | − | 20.4787i | 0.0135901 | − | 0.0235387i | ||||
\(871\) | −458.720 | + | 264.842i | −0.526659 | + | 0.304067i | ||||
\(872\) | 205.497 | + | 355.932i | 0.235662 | + | 0.408179i | ||||
\(873\) | −748.014 | − | 431.866i | −0.856832 | − | 0.494692i | ||||
\(874\) | − | 163.972i | − | 0.187611i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −75.4844 | −0.0861694 | ||||||||
\(877\) | 152.096 | − | 263.438i | 0.173427 | − | 0.300385i | −0.766188 | − | 0.642616i | \(-0.777849\pi\) |
0.939616 | + | 0.342231i | \(0.111182\pi\) | |||||||
\(878\) | 179.548 | − | 103.662i | 0.204496 | − | 0.118066i | ||||
\(879\) | −107.500 | − | 186.196i | −0.122299 | − | 0.211827i | ||||
\(880\) | −109.279 | − | 63.0924i | −0.124181 | − | 0.0716959i | ||||
\(881\) | 863.732i | 0.980400i | 0.871610 | + | 0.490200i | \(0.163076\pi\) | ||||
−0.871610 | + | 0.490200i | \(0.836924\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −567.456 | −0.642645 | −0.321323 | − | 0.946970i | \(-0.604127\pi\) | ||||
−0.321323 | + | 0.946970i | \(0.604127\pi\) | |||||||
\(884\) | 57.5147 | − | 99.6184i | 0.0650619 | − | 0.112691i | ||||
\(885\) | 159.529 | − | 92.1039i | 0.180258 | − | 0.104072i | ||||
\(886\) | −75.9153 | − | 131.489i | −0.0856831 | − | 0.148408i | ||||
\(887\) | 770.555 | + | 444.880i | 0.868721 | + | 0.501556i | 0.866923 | − | 0.498442i | \(-0.166094\pi\) |
0.00179783 | + | 0.999998i | \(0.499428\pi\) | |||||||
\(888\) | 5.96820i | 0.00672095i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −471.993 | −0.530329 | ||||||||
\(891\) | 160.246 | − | 277.554i | 0.179849 | − | 0.311508i | ||||
\(892\) | 213.442 | − | 123.231i | 0.239284 | − | 0.138151i | ||||
\(893\) | 110.140 | + | 190.767i | 0.123337 | + | 0.213625i | ||||
\(894\) | 81.1873 | + | 46.8735i | 0.0908136 | + | 0.0524312i | ||||
\(895\) | − | 1227.96i | − | 1.37202i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −304.191 | −0.339120 | ||||||||
\(898\) | −95.5736 | + | 165.538i | −0.106429 | + | 0.184341i | ||||
\(899\) | 148.742 | − | 85.8764i | 0.165453 | − | 0.0955243i | ||||
\(900\) | 160.971 | + | 278.809i | 0.178856 | + | 0.309788i | ||||
\(901\) | −182.316 | − | 105.260i | −0.202349 | − | 0.116826i | ||||
\(902\) | 188.106i | 0.208543i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 97.7056 | 0.108081 | ||||||||
\(905\) | 514.191 | − | 890.605i | 0.568167 | − | 0.984094i | ||||
\(906\) | 80.6512 | − | 46.5640i | 0.0890190 | − | 0.0513951i | ||||
\(907\) | −186.989 | − | 323.874i | −0.206162 | − | 0.357083i | 0.744340 | − | 0.667800i | \(-0.232764\pi\) |
−0.950502 | + | 0.310717i | \(0.899431\pi\) | |||||||
\(908\) | −132.286 | − | 76.3756i | −0.145690 | − | 0.0841141i | ||||
\(909\) | 506.395i | 0.557091i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1133.75 | 1.24451 | 0.622256 | − | 0.782814i | \(-0.286216\pi\) | ||||
0.622256 | + | 0.782814i | \(0.286216\pi\) | |||||||
\(912\) | −6.00000 | + | 10.3923i | −0.00657895 | + | 0.0113951i | ||||
\(913\) | 525.618 | − | 303.466i | 0.575704 | − | 0.332383i | ||||
\(914\) | −112.950 | − | 195.635i | −0.123577 | − | 0.214042i | ||||
\(915\) | −372.893 | − | 215.290i | −0.407533 | − | 0.235289i | ||||
\(916\) | 714.572i | 0.780101i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 66.7279 | 0.0726884 | ||||||||
\(919\) | −228.151 | + | 395.169i | −0.248260 | + | 0.429999i | −0.963043 | − | 0.269347i | \(-0.913192\pi\) |
0.714783 | + | 0.699346i | \(0.246525\pi\) | |||||||
\(920\) | 450.375 | − | 260.024i | 0.489538 | − | 0.282635i | ||||
\(921\) | 7.52900 | + | 13.0406i | 0.00817481 | + | 0.0141592i | ||||
\(922\) | −379.977 | − | 219.380i | −0.412122 | − | 0.237939i | ||||
\(923\) | 557.007i | 0.603474i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55.7948 | 0.0603187 | ||||||||
\(926\) | 230.527 | − | 399.284i | 0.248949 | − | 0.431193i | ||||
\(927\) | 883.124 | − | 509.872i | 0.952669 | − | 0.550024i | ||||
\(928\) | −9.94113 | − | 17.2185i | −0.0107124 | − | 0.0185545i | ||||
\(929\) | 824.058 | + | 475.770i | 0.887037 | + | 0.512131i | 0.872972 | − | 0.487770i | \(-0.162189\pi\) |
0.0140650 | + | 0.999901i | \(0.495523\pi\) | |||||||
\(930\) | − | 328.771i | − | 0.353518i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −546.146 | −0.585994 | ||||||||
\(933\) | 65.3011 | − | 113.105i | 0.0699904 | − | 0.121227i | ||||
\(934\) | 729.407 | − | 421.123i | 0.780949 | − | 0.450881i | ||||
\(935\) | 59.3269 | + | 102.757i | 0.0634513 | + | 0.109901i | ||||
\(936\) | −317.823 | − | 183.495i | −0.339555 | − | 0.196042i | ||||
\(937\) | − | 1295.71i | − | 1.38283i | −0.722460 | − | 0.691413i | \(-0.756989\pi\) | ||
0.722460 | − | 0.691413i | \(-0.243011\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −70.2578 | −0.0748219 | ||||||||
\(940\) | −349.316 | + | 605.033i | −0.371613 | + | 0.643652i | ||||
\(941\) | 1175.10 | − | 678.446i | 1.24878 | − | 0.720984i | 0.277915 | − | 0.960606i | \(-0.410357\pi\) |
0.970866 | + | 0.239622i | \(0.0770234\pi\) | |||||||
\(942\) | 4.28993 | + | 7.43038i | 0.00455407 | + | 0.00788788i | ||||
\(943\) | −671.382 | − | 387.622i | −0.711964 | − | 0.411052i | ||||
\(944\) | − | 154.882i | − | 0.164070i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 70.5442 | 0.0745710 | ||||||||
\(947\) | 354.731 | − | 614.412i | 0.374584 | − | 0.648799i | −0.615681 | − | 0.787996i | \(-0.711119\pi\) |
0.990265 | + | 0.139197i | \(0.0444522\pi\) | |||||||
\(948\) | 41.9848 | − | 24.2400i | 0.0442878 | − | 0.0255696i | ||||
\(949\) | −402.213 | − | 696.654i | −0.423828 | − | 0.734092i | ||||
\(950\) | 97.1543 | + | 56.0921i | 0.102268 | + | 0.0590443i | ||||
\(951\) | 345.784i | 0.363601i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 936.603 | 0.982794 | 0.491397 | − | 0.870936i | \(-0.336486\pi\) | ||||
0.491397 | + | 0.870936i | \(0.336486\pi\) | |||||||
\(954\) | −335.823 | + | 581.663i | −0.352016 | + | 0.609710i | ||||
\(955\) | −1424.72 | + | 822.564i | −1.49186 | + | 0.861324i | ||||
\(956\) | 265.103 | + | 459.171i | 0.277304 | + | 0.480305i | ||||
\(957\) | −10.3890 | − | 5.99807i | −0.0108558 | − | 0.00626757i | ||||
\(958\) | − | 716.554i | − | 0.747969i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −38.0589 | −0.0396447 | ||||||||
\(961\) | 713.477 | − | 1235.78i | 0.742432 | − | 1.28593i | ||||
\(962\) | −55.0812 | + | 31.8011i | −0.0572569 | + | 0.0330573i | ||||
\(963\) | 482.007 | + | 834.861i | 0.500527 | + | 0.866938i | ||||
\(964\) | −151.794 | − | 87.6383i | −0.157463 | − | 0.0909111i | ||||
\(965\) | − | 1023.42i | − | 1.06054i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1374.37 | 1.42127 | 0.710635 | − | 0.703561i | \(-0.248408\pi\) | ||||
0.710635 | + | 0.703561i | \(0.248408\pi\) | |||||||
\(968\) | 139.113 | − | 240.950i | 0.143711 | − | 0.248916i | ||||
\(969\) | 9.77208 | − | 5.64191i | 0.0100847 | − | 0.00582241i | ||||
\(970\) | −477.286 | − | 826.684i | −0.492048 | − | 0.852252i | ||||
\(971\) | 27.2466 | + | 15.7309i | 0.0280604 | + | 0.0162007i | 0.513965 | − | 0.857811i | \(-0.328176\pi\) |
−0.485904 | + | 0.874012i | \(0.661510\pi\) | |||||||
\(972\) | − | 322.467i | − | 0.331757i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 298.825 | 0.306802 | ||||||||
\(975\) | 104.059 | − | 180.235i | 0.106727 | − | 0.184857i | ||||
\(976\) | −313.529 | + | 181.016i | −0.321239 | + | 0.185467i | ||||
\(977\) | 270.949 | + | 469.297i | 0.277327 | + | 0.480345i | 0.970720 | − | 0.240215i | \(-0.0772181\pi\) |
−0.693392 | + | 0.720560i | \(0.743885\pi\) | |||||||
\(978\) | 195.047 | + | 112.611i | 0.199435 | + | 0.115144i | ||||
\(979\) | 239.445i | 0.244581i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1232.98 | −1.25687 | ||||||||
\(982\) | 554.485 | − | 960.397i | 0.564649 | − | 0.978001i | ||||
\(983\) | −19.4161 | + | 11.2099i | −0.0197519 | + | 0.0114038i | −0.509843 | − | 0.860267i | \(-0.670297\pi\) |
0.490092 | + | 0.871671i | \(0.336963\pi\) | |||||||
\(984\) | 28.3675 | + | 49.1340i | 0.0288288 | + | 0.0499329i | ||||
\(985\) | −1040.01 | − | 600.448i | −1.05584 | − | 0.609592i | ||||
\(986\) | 18.6957i | 0.0189611i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −127.882 | −0.129435 | ||||||||
\(989\) | −145.368 | + | 251.784i | −0.146984 | + | 0.254584i | ||||
\(990\) | 327.838 | − | 189.277i | 0.331149 | − | 0.191189i | ||||
\(991\) | −339.017 | − | 587.195i | −0.342096 | − | 0.592528i | 0.642726 | − | 0.766097i | \(-0.277804\pi\) |
−0.984822 | + | 0.173568i | \(0.944470\pi\) | |||||||
\(992\) | −239.397 | − | 138.216i | −0.241328 | − | 0.139331i | ||||
\(993\) | − | 161.429i | − | 0.162567i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2312.28 | −2.32390 | ||||||||
\(996\) | 91.5290 | − | 158.533i | 0.0918966 | − | 0.159170i | ||||
\(997\) | −758.779 | + | 438.081i | −0.761062 | + | 0.439400i | −0.829677 | − | 0.558244i | \(-0.811475\pi\) |
0.0686147 | + | 0.997643i | \(0.478142\pi\) | |||||||
\(998\) | 121.263 | + | 210.034i | 0.121506 | + | 0.210455i | ||||
\(999\) | −31.9523 | − | 18.4477i | −0.0319843 | − | 0.0184661i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 98.3.d.a.19.1 | 4 | ||
3.2 | odd | 2 | 882.3.n.b.19.2 | 4 | |||
4.3 | odd | 2 | 784.3.s.c.705.2 | 4 | |||
7.2 | even | 3 | 98.3.b.b.97.3 | 4 | |||
7.3 | odd | 6 | inner | 98.3.d.a.31.1 | 4 | ||
7.4 | even | 3 | 14.3.d.a.3.1 | ✓ | 4 | ||
7.5 | odd | 6 | 98.3.b.b.97.4 | 4 | |||
7.6 | odd | 2 | 14.3.d.a.5.1 | yes | 4 | ||
21.2 | odd | 6 | 882.3.c.f.685.2 | 4 | |||
21.5 | even | 6 | 882.3.c.f.685.1 | 4 | |||
21.11 | odd | 6 | 126.3.n.c.73.2 | 4 | |||
21.17 | even | 6 | 882.3.n.b.325.2 | 4 | |||
21.20 | even | 2 | 126.3.n.c.19.2 | 4 | |||
28.3 | even | 6 | 784.3.s.c.129.2 | 4 | |||
28.11 | odd | 6 | 112.3.s.b.17.1 | 4 | |||
28.19 | even | 6 | 784.3.c.e.97.2 | 4 | |||
28.23 | odd | 6 | 784.3.c.e.97.3 | 4 | |||
28.27 | even | 2 | 112.3.s.b.33.1 | 4 | |||
35.4 | even | 6 | 350.3.k.a.101.2 | 4 | |||
35.13 | even | 4 | 350.3.i.a.299.3 | 8 | |||
35.18 | odd | 12 | 350.3.i.a.199.2 | 8 | |||
35.27 | even | 4 | 350.3.i.a.299.2 | 8 | |||
35.32 | odd | 12 | 350.3.i.a.199.3 | 8 | |||
35.34 | odd | 2 | 350.3.k.a.201.2 | 4 | |||
56.11 | odd | 6 | 448.3.s.c.129.2 | 4 | |||
56.13 | odd | 2 | 448.3.s.d.257.1 | 4 | |||
56.27 | even | 2 | 448.3.s.c.257.2 | 4 | |||
56.53 | even | 6 | 448.3.s.d.129.1 | 4 | |||
84.11 | even | 6 | 1008.3.cg.l.577.2 | 4 | |||
84.83 | odd | 2 | 1008.3.cg.l.145.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.3.d.a.3.1 | ✓ | 4 | 7.4 | even | 3 | ||
14.3.d.a.5.1 | yes | 4 | 7.6 | odd | 2 | ||
98.3.b.b.97.3 | 4 | 7.2 | even | 3 | |||
98.3.b.b.97.4 | 4 | 7.5 | odd | 6 | |||
98.3.d.a.19.1 | 4 | 1.1 | even | 1 | trivial | ||
98.3.d.a.31.1 | 4 | 7.3 | odd | 6 | inner | ||
112.3.s.b.17.1 | 4 | 28.11 | odd | 6 | |||
112.3.s.b.33.1 | 4 | 28.27 | even | 2 | |||
126.3.n.c.19.2 | 4 | 21.20 | even | 2 | |||
126.3.n.c.73.2 | 4 | 21.11 | odd | 6 | |||
350.3.i.a.199.2 | 8 | 35.18 | odd | 12 | |||
350.3.i.a.199.3 | 8 | 35.32 | odd | 12 | |||
350.3.i.a.299.2 | 8 | 35.27 | even | 4 | |||
350.3.i.a.299.3 | 8 | 35.13 | even | 4 | |||
350.3.k.a.101.2 | 4 | 35.4 | even | 6 | |||
350.3.k.a.201.2 | 4 | 35.34 | odd | 2 | |||
448.3.s.c.129.2 | 4 | 56.11 | odd | 6 | |||
448.3.s.c.257.2 | 4 | 56.27 | even | 2 | |||
448.3.s.d.129.1 | 4 | 56.53 | even | 6 | |||
448.3.s.d.257.1 | 4 | 56.13 | odd | 2 | |||
784.3.c.e.97.2 | 4 | 28.19 | even | 6 | |||
784.3.c.e.97.3 | 4 | 28.23 | odd | 6 | |||
784.3.s.c.129.2 | 4 | 28.3 | even | 6 | |||
784.3.s.c.705.2 | 4 | 4.3 | odd | 2 | |||
882.3.c.f.685.1 | 4 | 21.5 | even | 6 | |||
882.3.c.f.685.2 | 4 | 21.2 | odd | 6 | |||
882.3.n.b.19.2 | 4 | 3.2 | odd | 2 | |||
882.3.n.b.325.2 | 4 | 21.17 | even | 6 | |||
1008.3.cg.l.145.2 | 4 | 84.83 | odd | 2 | |||
1008.3.cg.l.577.2 | 4 | 84.11 | even | 6 |